The 24-year-old, who marked the end of his injury misery with a goal on his return to action on Sunday, needed just 21 minutes to double his tally for the season with a sumptuous volley which set the Black Cats on their way to a resounding Premier League victory.
Stephane Sessegnon added a second seven minutes later and the points were safe nine minutes into the second half when Phil Bardsley's cross ended up in the back of the net with the help of deflections off defender Daniel Ayala and keeper John Ruddy.
The win extended manager Martin O'Neill's run since he replaced Steve Bruce to just two defeats in 11 games in all competitions and extended his side's points tally to 30 - one more than the visitors - to the delight of a crowd of 34,476.
For City manager Paul Lambert, who played under the Ulsterman at Celtic, his night in the North-East proved a sobering experience as his men failed to scale the heights they have done for much of the campaign to date.
O'Neill spent the final days of the transfer window frantically searching for a striker to bolster his depleted attacking resources, as well as defenders to shore up his team at the back.
In the event, he was only partially successful as Wayne Bridge and Sotirios Kyrgiakos arrived on loan, but no frontman.
He need not have worried.
The game was effectively won inside the opening 28 minutes as Norwich, who had previously made such a good fist of their first season in the top flight, simply found Campbell and Sessegnon too hot to handle.
Campbell, who ended his 17th-month fitness nightmare with a vital equaliser in his side's FA Cup fourth round draw with Middlesbrough, had already served warning of his intent, having forced Bradley Johnson to block a first-minute effort and then called upon Ruddy for the first time with a close-range header four minutes later.
But the visitors did not heed the warnings and fell behind with 21 minutes gone, in spectacular style.
Winger James McClean lifted the ball over full-back Russell Martin as he cut inside and although the defender managed to nudge it away from him, Campbell controlled before smashing a dipping volley over Ruddy and into the back of the net.
But there was better to come just seven minutes later as Sunderland cut a swathe through the green shirts.
Michael Turner's defensive header dropped to Sessegnon inside his own half, and he earned himself a cheer from the home fans when he cheekily pushed the ball through the hapless Johnson's legs.
Not content with that, the Benin international slid a pass out to Campbell on the right and then continued his run into the box to meet the striker's cross with a downward header which Ruddy was powerless to keep out.
Norwich had offered little as an attacking force, but they might have taken the lead themselves with 13 minutes gone.
Steve Morison got up well to flick on Kyle Naughton's free-kick and Grant Holt sent in a volley which keeper Simon Mignolet could only parry.
Turner blocked Morison's follow-up and Andrew Surman blasted the loose ball high and wide, but that scare was one of few O'Neill's side suffered during a first half which they largely dominated.
The visitors showed little sign of reversing the trend in the opening stages of the second half, with only Naughton's intervention denying Campbell a free run at goal after McClean had robbed Wes Hoolahan and skipped past Ayala before finding Sessegnon.
Ruddy had to pull off a fine 50th-minute save to keep out Craig Gardner's first-time shot with Sebastian Larsson the provider, and it seemed only a matter of time before the home side struck again.
The third goal duly arrived within four minutes when full-back Bardsley burst into the box and drilled in a low cross which Ayala could only turn on to his keeper and into his own net.
Campbell came agonisingly close to making it 4-0 when he only just failed to connect with Larsson's 59th-minute cross after leaving the Canaries defence in his wake.
Morison headed substitute Anthony Pilkington's 64th-minute cross just wide, but Gardner went equally close from distance at the other end seconds later.
Campbell departed to rapturous applause when he was replaced by Ji Dong-won with 16 minutes remaining having more than accomplished his task for the night, and O'Neill was able to hand Bridge a debut as a late substitute.